Circle Calculator
Calculate a circle's radius, diameter, circumference and area from any single known value.
| Property | Formula | Value |
|---|---|---|
| Radius | r | 5 |
| Diameter | 2r | 10 |
| Circumference | 2πr | 31.4159 |
| Area | πr² | 78.5398 |
Every circle measurement is derived from the same radius — this table shows exactly which formula produces each one.
- Diameter10
- Circumference31.4159
- Area78.5398
About the Circle Calculator
A circle's radius, diameter, circumference and area are all locked to each other by fixed formulas, which means knowing any single one of them is enough to work out all the rest. That's useful anywhere only one measurement is easy to take directly — measuring the distance around a round table (circumference) to find its diameter for a tablecloth, or knowing a pipe's stated diameter and needing its cross-sectional area for a flow calculation.
This calculator takes whichever one of the four values you already know and derives the other three, so there's no need to remember and rearrange four different formulas by hand.
How it’s calculated
Everything about a circle flows from the radius r, the distance from the center to the edge. Diameter is simply twice the radius (d = 2r). Circumference, the distance around the circle, is 2πr. Area, the space enclosed, is πr². If you start from something other than the radius, this calculator first solves for r (dividing diameter by 2, dividing circumference by 2π, or taking the square root of area divided by π) and then derives the rest from there.
π (pi) is the fixed ratio between any circle's circumference and its diameter — roughly 3.14159, and the same for every circle regardless of size. It's an irrational number, so it never terminates or repeats, which is why calculations use a rounded approximation rather than an exact value.
Frequently asked questions
How do I find the radius from the circumference?
Divide the circumference by 2π. Since circumference = 2πr, solving for r gives r = circumference / (2π). A circle with a 31.4-inch circumference has a radius of about 5 inches.
What's the formula for the area of a circle?
Area = πr², where r is the radius. Doubling the radius doesn't double the area — it quadruples it, since the radius is squared in the formula.
What's the difference between circumference and perimeter?
They mean the same thing — the distance around the outside of a shape — but 'circumference' is the term specifically reserved for circles, while 'perimeter' is the general term used for polygons and other shapes.
What value of pi does this calculator use?
The full double-precision value built into JavaScript's Math.PI (roughly 3.14159265358979), which is far more precise than the 3.14 or 22/7 approximations commonly used by hand, so results here won't drift for larger circles the way hand-rounded pi can.
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